Problem: Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{q^2 + q - 90}{q^2 + 10q}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{q^2 + q - 90}{q^2 + 10q} = \dfrac{(q - 9)(q + 10)}{(q)(q + 10)} $ Notice that the term $(q + 10)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(q + 10)$ gives: $y = \dfrac{q - 9}{q}$ Since we divided by $(q + 10)$, $q \neq -10$. $y = \dfrac{q - 9}{q}; \space q \neq -10$